Find the equation of the linear function represented by the table

Find the equation of the linear function represented by the table below in slope-intercept form.
x y
1 -2
2 -1
3 0
4 1

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Take any two points and find the slope of the line through the two points.

change in y
——————— = slope
change in x

(1,-2) and (2,-1) {the first two points}

-1 - (-2)
————— = slope {change in y over change in x}
2 - 1

1
— = slope {simplified numerator and denominator}
1

slope = 1 {reduced}

Take the slope, along with one of the points, and substitute into slope-intercept form,
in order to find the y-intercept of the line.

Slope-intercept form is y = mx + b
m is the slope
b is the y-intercept

(1,-2) , slope = 1
y = mx + b {slope-intercept form}
-2 = 1(1) + b {substituted 1 in for x, -2 for y, and 1 for m}
-2 = 1 + b {multiplied 1 by 1}
b = -3 {subtracted 1 from each side}

Substitute the slope and y-intercept back into slope-intercept form.

y = mx + b {slope-intercept form}
y = 1x - 3 {substituted 1 for m, and -3 for b}
y = x - 3 {dropped the 1 from in front of the x}

y = x - 3 is the equation of the function represented by the table

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